(CNN) -- Foreigners are making a run to get out of volatile Libya, with thousands hustling to the Egyptian border and foreign governments scrambling to help their citizens.

Around 12,000 people have crossed into Egypt from Libya, officials say, in an effort to flee the violence engulfing the North Africa nation.

"There is no security over there," said Esat Abubakr, an Egyptian living in Benghazi said after he arrived in Sollum, Egypt.

He described widespread violence and a climate of fear with no security. He said people drove to the border and then walked across.

"Every Egyptian I know is trying to come back to Egypt," he said.

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Lt. Col. Raouf Ezzat, an Egyptian military doctor overseeing medical care of the fleeing people, said the army is permitting only Egyptian citizens and Libyans married to Egyptians to enter Egypt.

But he said anyone wounded would be treated. "Any patient that comes to me, whether Egyptian or Libyan, I will treat them," he said, adding that any wounded Libyan who arrived at the border asking for help would be allowed to enter and be treated.

Ten Egyptians with minor injuries arrived Tuesday from different parts of Libya, but authorities were expecting and preparing for large numbers of injured people.

About 30 military doctors and 80 to 100 ambulances were stationed at the border, where an operating room was set up and 1,000 units of blood were en route.

The French Foreign Ministry said that it had sent three planes to Libya to help repatriate French citizens and that its embassy in Tripoli was helping to get citizens to the airport.

The Dutch military was responding as well.

A Dutch Defense Ministry spokesman told CNN that "a Dutch military plane has been authorized to land in Tripoli today to evacuate about 100 Dutch nationals" and a NATO commander said a Dutch frigate is heading there as well.

Britain said its citizens who don't have "a pressing need to remain in the country should leave by commercial means if it is safe to do so." Britain also "is looking urgently into options for possible charter flights."

The government was advising Britons who want to leave Libya but can't buy tickets online "to travel to the airport carrying sufficient cash to buy tickets. Problems with internet connections in Libya mean that electronic payments may not be accepted."

The United States was unable to move any Americans out of Libya on Tuesday, said State Department spokesman P.J. Crowley.

Every Egyptian I know is trying to come back to Egypt.-- Egyptian living in Benghazi, Libya.

The State Department issued a travel alert for non-essential staff to leave the country, an order affecting 35 employees and their families.

There are other American citizens in Libya who might want to leave; some of them might be employees of energy companies that have suspended operations.

Of the several thousand U.S. citizens in Libya, most are dual nationals; those solely with U.S. citizenship number about 600, Crowley said.

The U.S. State Department was not able to land charter aircraft in Tripoli to fly out U.S. citizens because Libyan authorities did not give permission for those aircraft to land, said a senior administration official not authorized to speak for attribution.

The State Department was chartering ferries to take travelers from Tripoli's As-shahab port to Valletta, Malta on Wednesday, the official said, adding, "Tomorrow the question will be if they let the ferry dock. If that happens, our people will flow out."

Crowley said the airport in Tripoli remained open in "challenging" circumstances. International carriers, he said, were making more seats available for departure.

Oil companies, such as Total, BP, OMV and BP, said they would or planned to evacuate people some staff and families.

Libya's official Jana news agency reported that airport authorities said Libyan airspace was open to civilian aviation and was operating normally, contrary to the rumors broadcast by "conspiring media channels."

One Air Malta official -- who declined to be identified in keeping with company policy -- said thousands were waiting at Tripoli's airport for a flight out.

British Airways and BMI flights in and out of Tripoli have been canceled. Both companies said they were monitoring the situation closely.

The British Foreign Office confirmed the cancellations and said KLM also canceled its Tuesday flights. It said Turkish Airlines, Air Malta, Alitalia, Austrian and Egypt Air "are operating flights but these are all full at present."

Air Malta said a Malta-bound flight finally left Tripoli International Airport after it had been delayed because of heavy congestion there.

Turkish Prime Minister Recep Tayyip Erdogan said Turkey couldn't land its planes and was sending a ship and two ferry boats for evacuations.

"Since there was no one in the control tower (at Benghazi airport), landing was not allowed. It was also not possible to land in Tripoli," he said.